Reduced FFT-Based Simulation of a Mechanically Loaded Clustered Microstructure Using an Adaptive Set of Fourier Modes

Abstract

Processes, such as deep rolling or induction hardening, have a remarkable influence on the material properties within the surface layer of a work piece. Our overall goal is to develop efficient two-scale methods, which are able to show the microstructural evolution of the machined material. The calculation of a spatially resolved microstructure comes along with a high computational effort. To reduce the computational costs, we combine a clustered description of the structure [1] with a model order reduction technique for the performed fast Fourier transformations (FFT) [2]. We choose a reduced set of Fourier modes, which is adapted to the underlying microstructure and thus based on the occurring strain field [3]. By that, we analyze the influence of a mechanical impact on an elasto-plastically deforming material.

FFT‐based simulation of evolving microstructures utilizing an adapting reduced set of Fourier modes

“…In this context, interesting topics are related to decreasing the computational effort of the stress evaluations (e.g. by using a clustered microstructure [20,36] for the stress evaluations in real space [32]), using more efficient solvers (e.g. Nesterov's fast gradient method [26] or the Heavy ball method [1]), or reducing the effect of Gibbs oscillations [3] on the convergence behavior (e.g.…”

Efficient thermomechanically coupled FE‐FFT‐based multiscale simulation of polycrystals

“…Since model order reduction techniques are widely used for macroscale simulations, only specific model order reduction techniques applied to FFT‐based microscale simulations are addressed here. In this context, the computational costs of FFT‐based microscale simulations have been reduced using proper orthogonal decomposition [27], low‐rank tensor approximations [28], or a reduced set of Fourier modes [29] with a fixed [29], geometrically adapted [30], or strain‐based [31] sampling pattern, or additionally combined with a clustered microstructure [32].…”

Efficient monolithic solution of FE2 problems

“…[3], [40], [45], however directly ensures a physical material description especially under irreversible behavior, because it keeps the properties of the original FE 2 model without the need for special considerations, which is why this article only focuses on this approach. It is worth mentioning, that a similar method was also proposed for the FFT formulation, whereby in complete analogy a reduced set of Fourier Modes is constructed and a lower set of integration points is chosen [47]. Other sophisticated methods relying also on the reduced basis approach but moving further away from the FE 2 idea towards hybrid approaches e.g.…”